Critical behavior of the Random-Field Ising Magnet with long range correlated disorder

TL;DR

This study investigates the critical behavior of the Random-Field Ising Magnet with long-range correlated disorder, revealing similar critical properties to uncorrelated disorder but with notable differences in susceptibility and a potential phase transition at infinitesimal disorder for a=-1.

Contribution

It provides the first comprehensive numerical analysis of the RFIM with long-range correlated disorder, extending understanding of critical phenomena in disordered magnetic systems.

Findings

Critical exponents similar to uncorrelated RFIM for most a values.

Finite-size susceptibility exponent differs with disorder correlation.

Possible phase transition at infinitesimal disorder for a=-1.

Abstract

We study the correlated-disorder driven zero-temperature phase transition of the Random-Field Ising Magnet using exact numerical ground-state calculations for cubic lattices. We consider correlations of the quenched disorder decaying proportional to r^a, where r is the distance between two lattice sites and a<0. To obtain exact ground states, we use a well established mapping to the graph-theoretical maximum-flow problem, which allows us to study large system sizes of more than two million spins. We use finite-size scaling analyses for values a={-1,-2,-3,-7} to calculate the critical point and the critical exponents characterizing the behavior of the specific heat, magnetization, susceptibility and of the correlation length close to the critical point. We find basically the same critical behavior as for the RFIM with delta-correlated disorder, except for the finite-size exponent of the susceptibility and for the case a=-1, where the results are also compatible with a phase transition at infinitesimal disorder strength. A summary of this work can be found at the papercore database at www.papercore.org.